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CHAPTER CAPITAL BUDGETING−PART I 7-1 Risk and Capital Investments Colgate faces lower risk than J&J because it is expanding production of an existing, and successful, product The major risk is that the product will become less popular and sales will not materialize The new plant could also be too costly, but that seems unlikely as the technology to make consumer products is well-established J&J faces risks that the drug will not prove efficacious, that the Food and Drug Administration will not approve it, or that another company will develop a better drug One reason we use this example is to make the point that R&D is just like any other investment, except that no depreciation is involved 7-2 Payback and Risk Either voyage is acceptable, but most students will probably select the shorter, safer one A lot can happen to a ship on a long voyage−storms, piracy, or collisions with icebergs or rocks Considering the hazards, who wouldn't feel a lot safer tying up his or her money for one year rather than five despite the advantage of the longer voyage as determined under the normal techniques of analysis? Whether you would choose to invest in the one-year or the fiveyear opportunity depends on your attitude about risk and return Because of its emphasis on the rapidity of return of investment, the payback method of evaluation gives higher priority to the one-year voyage 7-3 Government Actions and Capital Investment Investment will increase because net cash flows will increase and more projects will meet DCF criteria Some students might ask about the value of depreciation deductions, which will fall, but after-tax cash flows from savings or higher sales will more than offset lower tax shields Investment will increase because cost of capital will decrease investments will meet companies’ capitalbudgeting criteria More Investments will increase because cash savings from depreciation will be immediate rather than spread out over the life of an asset You might wish to discuss ACRS and MACRS at this point, perhaps pointing out that lives for tax purposes are significantly shorter than economic lives for most assets Investment should increase as it becomes profitable to substitute capital for labor Investments will increase because as labor becomes costlier, companies will substitute capital, just as in item We tried to be very explicit about the effects in this question because we have used it as an exam question and gotten disappointing results Most students say that investments will decrease because the company will have less cash to invest, which ignores external financing 7-1 7-4 Capital Budgeting−Effects of Events An increase in labor rates makes labor-cost-saving projects more attractive, but makes increasing output less attractive Increasing output might still be attractive, but not as much as it would have been with lower labor costs First, we have to assume that we will either reduce prices to meet the competition, or lose volume If we expect to hold prices and lose volume, cost-saving investments become less desirable because they affect fewer units (assuming that the savings are in variable costs) Certainly, decisions to increase output will be much less desirable because the volume will not be as high as originally forecast If we meet the price reductions, decisions to increase output will be less desirable because the contribution margin from the additional sales will be lower than otherwise Cost-reduction investments will probably be unaffected Investments that reduce costs become more attractive, because cost reduction is critical in mature industries Investments that increase output become less attractive because the volume increases will be less than anticipated 7-5 Qualitative Concerns General Note to the Instructor: The purposes of this and the following question are (a) to encourage students to think about both the quantitative and qualitative aspects of making decisions, and (b) to reduce students' concentration on the mechanics of specific analytical techniques The two questions should probably be considered together, since one deals with rejecting a project that is economically acceptable while the other deals with accepting a project deemed economically unacceptable We introduce capital rationing, sensitivity analysis, and mutually exclusive alternatives in Chapter We leave to courses in managerial finance the task of discussing the significance and calculation of cost of capital and the use of risk-adjusted discount rates Nevertheless, we have found that, if pushed, most groups of students will come up with ideas encompassing most of the problematic aspects of capitalbudgeting decisions not covered in the current chapter The list of reasons we offer below is not all-inclusive but generalizes the points made by past students a Top-level managers might object, in principle, to owning a tobacco farm (Chapter noted that convictions of managers could affect their decisions.) b Estimates about the success of the farm might vary widely and include a significant probability of a large loss (At this point, students might express a lack of confidence in the estimates producing the positive NPV.) The furor over tobacco in recent years lends an air of uncertainty as to the future of the industry c The company might have many other projects with higher returns and not be able to fund all projects that are acceptable (Students are usually quick to raise the issue of limited funds, or capital rationing.) d The company might use other screens for its projects, such as a minimum IRR or a maximum payback period, and this project might not meet those cutoffs (Chapter suggests that a company might establish such cutoffs.) 7-2 The general note at the beginning also applies here, but this introduces some additional ideas a The project involves a product the company's top managers believe is needed to round out its product line (This reason relates to an overall issue and could prevail even if analysis of the project gives full consideration to complementary effects.) b The project could involve a change in the manufacturing process to meet mandated pollution or hazardous-waste disposal guidelines (This answer assumes that reasonable alternatives for meeting the guidelines produce lower IRRs, and that management has consciously decided the company should not abandon the area of its business affected by the mandated guidelines.) c The project could involve improving employee relations (e.g., a cafeteria, a recreation facility) or some other issue on which the company might have already committed itself to making changes with the expectation of selecting projects with the "lowest cost." (A project showing a 20% IRR is clearly better than one showing an 8% return.) d The project might advance an important strategy If the company's reputation for high-quality products includes a role as an innovator, the project might be accepted to retain the company's competitive edge, despite the company's inability to quantify the advantages of maintaining that role If reducing cycle time, or improving logistics, is critically important, the company might well accept a project that advances such a strategy, even without favorable numbers e Managers might believe that the combination of an attractive payback period, relatively low risk, and their gross assessments of positive and negative nonquantifiable factors offsets its lower IRR (Most students are likely to come up with this technique-related answer.) 7-6 Discounting (a) (15 minutes) About 12% Investment Divided by cash flow Present value factor annuity of years Factor for 12% (b) About 12% Investment Divided by cash flow Present value factor, years Factor for 12% 7-7 $60,000 $12,000 5.000 4.968 (a) $9,500 [($30,000 x 5.650) - $160,000] (b) Negative $3,436 Discounting $120,000 $150,000 800 797 [($8,000 x 3.037) + ($4,000 x 567) - $30,000] (10 minutes) $34,050, the present value of $50,000 five years hence at 8% ($50,000 x 681) $66,096, PV of a 4-year annuity of $20,400 at 9% ($10,200 x 3.240) 7-3 He should take the $700,000 lump sum because the present value of the annuity is only $671,000 ($100,000 x 6.710) Of course, if he lives longer, he has a serious problem 7-8 $2,298,755 ($167,000 x 13.765, the factor for 30 periods at 6%) Time Value of Money Relationships (10-15 minutes) Just about $8,000 $12,880 x 621, the factor for 10% and years years $20,000/$54,000 $45,640 $10,000 x 4.564, the factor for 12% and years = 370, the factor for 18% and years 4 years $100,000/$34,300 = 2.915 factor for 14% and four years, 2.914 7-9 This factor is nearly equal to the About $35,398, $200,000/5.65, the factor for 10 years at 12% NPV and IRR Methods (10 minutes) $2,220 Annual cash return Times present value factor for 4-year annuity at 10% Present value of flows Less required investment Net present value A bit over 18% Required investment Divided by annual cash flow Equals relevant PV factor for 4-year annuity PV factor for 4-year annuity at 18% 7-10 Basic CapitalBudgeting Without Taxes $18,800 $ 7,000 2.686 2.690 (15 minutes) $39,550 Cash savings Present value factor, years, 10% Present value of future flows Investment Net present value About 20% $150,000/$50,000 = 3.0 = factor for five years closest factor is 2.991, the factor for 20% $ 7,000 3.170 $22,190 18,800 $ 3,390 Cash Flow $ 50,000 3.791 $189,550 150,000 $ 39,550 The 3.0 years, as calculated in requirement 27%, income of $20,000 ($50,000 - $30,000 depreciation) divided by $75,000 average investment Note to the Instructor: We stated that Ms Pawl wanted a 10% return from the business because an entrepreneur such as she would probably not speak of cost of capital or cutoff rates You might want to delve into how a small business operator might make such judgments 7-4 7-11 Basic CapitalBudgeting Taxes (Extension of 7-10) (15 minutes) $16,804 Tax $50,000 30,000 20,000 $ 6,000 Pretax cash flow Depreciation ($150,000/5) Increase in pretax income Income tax at 30% Net cash flow Present value factor, years, 10% Present value of future flows Investment Net present value Cash Flow $ 50,000 6,000 $ 44,000 3.791 166,804 150,000 $ 16,804 About 14% $150,000/$44,000 = 3.409 = the factor for five years closest factor is 3.433, for 14% The IRR is therefore a bit over 14% 3.41 The years, as calculated in requirement 18.7%, income of $14,000 ($20,000 - $6,000) divided by the $75,000 average investment 7-12 Basic Cost Savings (10-15 minutes) $107,400 Tax Cash savings (200,000 x $2.25) Cash fixed costs Pretax cash flow Depreciation ($500,000/4) Increase in pretax income Income tax at 40% Net cash flow Present value factor, 12%, years Present value of future flows Investment Net present value $450,000 200,000 250,000 125,000 125,000 $ 50,000 Cash Flow $450,000 200,000 250,000 50,000 $200,000 3.037 $607,400 500,000 $107,400 NPV increases $9,540, the present value of the after-tax cash from the $25,000 residual value to be received years hence ($25,000 x 60% x 636), since the company can ignore salvage value for depreciation Note to the Instructor: This is a good time to remind the class that the sooner flows come in, the better The total tax savings from the asset are the same whether or not salvage value is included in the depreciation calculations But leaving salvage value out accelerates the savings, which are partly repaid when the gain is realized and taxed 7-13 Basic CapitalBudgeting −Services (10-15 minutes) $86,600 Cash operating savings Present value factor, years, 14% Present value of future flows Investment 7-5 Cash Flow $200,000 3.433 $686,600 600,000 Net present value $ 86,600 Nearly 20% The factor is 3.0 ($600,000/$200,000), which is closest to 2.991, the factor for 20% Because the 3.0 is greater than the 20% factor, the IRR is less than 20% 3 years, as calculated in requirement About 27%, income of $80,000 ($200,000 - $120,000 depreciation) divided by $300,000 average investment 7-14 Basic CapitalBudgeting With Taxes (Extension of 7-13) (10 minutes) Negative $23,260 Tax $200,000 120,000 80,000 $ 32,000 Cash savings Depreciation ($600,000/5) Increase in pretax income Income tax at 40% Net cash flow Present value factor, 14%, five years Present value of future flows, rounded Investment Net present value Cash Flow $200,000 32,000 168,000 3.433 $ 576,740 600,000 ($ 23,260) The IRR is a bit over 12% The factor is 3.571 ($600,000/$168,000), which is closest to 3.605, the 12% factor 3.571 years, as calculated in requirement 16%, income of $48,000 ($80,000 - taxes of $32,000) divided by $300,000 average investment 7-15 (a) (b) Comparison of Methods (20 minutes) A 2.0 years B 2.6 years C 3.5 years C, B, A Average income Divided by average investment $70,000/2 Equals book rate of return (c) B, C, A A $ 1,250 B $10,000 C $12,500 $35,000 3.6% $35,000 28.6% $35,000 35.7% Investment B is the only one with a positive NPV A Present Year Cash Flow Value $35,000 $30,170 35,000 26,005 0 5,000 2,760 Total $58,935 Investment 70,000 NPV ($11,065) B Cash Flow $35,000 10,000 45,000 20,000 7-6 C Present Value* $30,170 7,430 28,845 11,040 $77,485 70,000 $ 7,485 Cash Flow $ 4,000 8,000 10,000 98,000 Present Value $ 3,448 5,944 6,410 54,096 $69,898 70,000 ($ 102) * Present value factors are 862, 743, 641, and 552 The results show that payback and book-rate-of-return rankings not necessarily indicate relative profitability B is the only desirable investment, using discounted cash flow analysis Investment A illustrates that payback ignores profitability; the project has the quickest payback but little cash flow after the payback period Investment C has high income, but much of it comes in the last year, when the cash flow is worth less than it would have been earlier Investment C returns more in total than does A, but the wait is too long to be worthwhile at 16% 7-16 NPV (15-20 minutes) Sites should acquire the machine because its NPV is $28,848 Cost savings: Current cost (40,000 x $0.80) Expected cash cost [$8,400 + (40,000 x $0.10)] Annual savings Depreciation ($20,000/5) Pretax income Tax at 30% Net cash flow Present value factor, years, 16% Present value of future flows Less investment Net present value Tax Cash Flow $32,000 12,400 $19,600 4,000 15,600 $ 4,680 $32,000 12,400 19,600 4,680 $14,920 3.274 $48,848 20,000 $28,848 At least two nonquantitative factors might influence the decision The owner might view employing high school students as a contribution to the community and so be inclined not to purchase the new equipment However, with such a high NPV, it is unlikely that he would forego the purchase He would tend to favor the purchase even if it appeared marginally profitable, if he had experienced problems finding reliable students Note to the Instructor: This exercise has several purposes First, it requires students to determine the cost savings, information that is provided in most other assignments Second, it forces consideration of qualitative issues in a setting students are likely to understand 7-17 a CapitalBudgeting for a Not-for-Profit (20 minutes) $138,880 Annual cash flow ($300,000 - $120,000) Present value factor, 10 years, 14% Present value of future flows Investment Net present value $180,000 5.216 $938,880 800,000 $138,880 b 4.44 years ($800,000/$180,000) c About 18%, the factor for 18% is 4.494 for students using tables 7-18 Understanding IRR (15-20 minutes) General Note to the Instructor: 7-7 The purpose of this exercise is to trace the flows so that the student can see why the IRR is the interest rate that brings the NPV to zero $49,740, which is $20,000 x 2.487 (the factor for 10%, years) Beginning Balance + Interest at 10% - Withdrawal = Ending Balance $49,740 $4,974 $20,000 $34,714 34,714 3,471 20,000 18,185 18,185 1,819 20,000 The $4 difference results from rounding 7-19 NPV and IRR (10-15 minutes) ($9,240) Cash savings (200,000 x $2) Depreciation ($1,000,000/4) Increase in pretax income Income tax at 40% Net cash flow Present value factor, 14%, years Present value of future flows Investment Net present value Tax $400,000 250,000 150,000 $ 60,000 $ Cash Flow 400,000 60,000 340,000 2.914 990,760 1,000,000 ($ 9,240) $ About 13.5% from Lotus 1-2-3 The factor is 2.941 ($1,000,000/$340,000), which is close to the 2.914 factor for 14% 7-20 Relationships (d) (e) (b) (20-25 minutes) 20%, the factor for 20%, 10 years is 4.192 Cost Divided by annual cash flow Present value factor for 10 years $188,640 $ 45,000 4.192 $46,080 Annual cash flow Times the present value factor for 14%, 10 years Present value of future cash flows Less cost Net present value $ 45,000 5.216 $234,720 188,640 $ 46,080 $337,050 Annual cash flow Times present value factor for 18%, 10 years Cost (e) (a) $ 75,000 4.494 $337,050 $86,700 Annual cash flow Times present value factor for 12%, 10 years Present value of future cash flows Less cost Net present value $ 75,000 5.650 $423,750 337,050 $ 86,700 $62,073 Cost $300,000 7-8 Divided by the present value factor, 16%, 10 years Equals annual cash flow (c) 4.833 $ 62,073 10%, the factor for 10%, 10 years is 6.145 Cost Plus net present value Total present value of future cash flows Divided by annual cash flow Equals present value factor for 10 years (a) $300,000 81,440 $381,440 $ 62,073 6.145 $100,000 Cost Plus net present value Total present value Divided by present value factor for 12%, 10 Equals annual cash flow (d) $450,000 115,000 $565,000 5.650 $100,000 years About 18%, the factor for 18%, 10 years is 4.494 Cost Divided by annual cash flow Equals present value factor for 10 years 7-21 Comparison of Book Return and NPV $450,000 $100,000 4.500 (15-20 minutes) The hand-fed machine has the higher book rate of return on average investment Revenue (200,000 x $10) Variable costs at $4, $2 Cash fixed costs Depreciation ($800,000/4; $1,400,000/4) Total costs Pretax profit Income tax at 40% Net income Average investment $800,000/2 $1,400,000/2 Book rate of return Hand-Fed $2,000,000 800,000 725,000 200,000 1,725,000 275,000 110,000 $ 165,000 $ Semiautomatic $2,000,000 400,000 850,000 350,000 1,600,000 400,000 160,000 $ 240,000 400,000 $ 41.25% 700,000 34.3% The semiautomatic machine has the higher NPV Hand-Fed Net cash flows: Net income Depreciation Net cash flow Present value factor, years, 14% Present value Investment Net present value $ 165,000 200,000 $ 365,000 2.914 $1,063,610 800,000 $ 263,610 Semiautomatic $ 240,000 350,000 $ 590,000 2.914 $1,719,260 1,400,000 $ 319,260 The hand-fed machine has an IRR in excess of 25%; the semiautomatic machine's IRR is between 24% and 25% 7-9 Investment Divided by annual cash flows (part 2) Equals present value factor for years Closest factors: 25% 24% $ $ Hand-Fed 800,000 365,000 2.192 Semiautomatic $1,400,000 $ 590,000 2.373 2.362 2.362 2.404 Note to the Instructor: The above answer assumes students will limit their search for an answer to the tables available in the text IRR on the hand-fed machine is between 29% and 30% 7-22 Increasing Volume (15-20 minutes) $2,780 thousand Tax $ 7,500 4,200 3,300 2,000 1,300 $ 520 Contribution margin [(300 x ($90 - $65)] Fixed cash operating costs Pretax cash flow Depreciation ($8,000,000/4) Increase in taxable income Increased taxes (40%) Increase in net cash flow Cash Flow $ 7,500 4,200 3,300 520 $2,780 $443 thousand Increase in annual cash flow (requirement 1) Present value factor, years, 12% Present value of future cash flows Investment Net present value $ 2,780 3.037 $ 8,443 8,000 $ 443 14.6% from Lotus 1-2-3 For students using tables, the factor is 2.878 ($8,000/$2,780), which falls between the values for 14% and 16% NPV increases by $229 thousand Salvage value Less tax at 40% Net cash flow Times factor for years at 12% Equals present value of salvage value 7-23 Investing in JIT $600 240 360 636 $229 (15 minutes) $1,390 thousand Annual savings Less tax, at 40% Net flow Present value factor, 30 years, 10% Present value of flow Tax shield ($4.5 million/5) Tax rate Tax saving Present value factor, years, 10% Present value of tax savings Total present value of future flows Less investment Net present value 7-10 $ 800 320 $ 480 9.427 $4,525 $ 900 40% $ 360 3.791 1,365 5,890 4,500 $1,390 Note to the Instructor: This assignment doesn't get into the details of benefits that JIT provides, but it can serve as a basis for discussing JIT operations and how to measure some of their benefits The $800 thousand stated savings can come from any number of areas including lower material and labor costs, and lower costs for such support activities as inspection, materials-handling, maintenance, and production scheduling Some of these costs are relatively easy to estimate and some are not Among the costs of quality that should drop are the costs of warranties, field engineering, and other elements that result from having less than superb quality Other qualitative factors that managers should consider include higher productivity as workers become more involved and more satisfied, and higher sales because of increased quality The importance of any such factor depends on how well the company was doing before In some cases the incremental benefit could be quite high, in others relatively low 7-24 Safety Equipment (15 minutes) The NPV is a negative $8,051 Savings in premiums ($93,000 - $45,000) Depreciation ($200,000/10) Increase in taxable income Increased taxes at 40% Increase in net cash flow Present value factor, 10 years, 14% Present value of future cash flows Investment required Net present value Tax $48,000 20,000 28,000 $11,200 Cash Flow $ 48,000 11,200 36,800 5.216 191,949 200,000 ($ 8,051) The items covered in students' memos will differ, but the most likely recommendation is to install the equipment despite its negative NPV Memos should include some of the following items (a) The analysis understates the cost savings because it does not consider the potential for liability claims if employees are injured (or worse) The analysis should include some estimate of the potential savings from not increasing the potential losses in lawsuits brought by injured employees (b) The increased potential for injury to employees should be, in itself, a consideration in the decision Moreover, the cost to the company is relatively small (The cost of the new system is $200,000, suggesting a much larger value for the building and its contents, and this factory is only one of several owned by the company.) (c) Another factor to consider in connection with the increased potential for injury to employees is the potential for damage to the company's public image and reputation if the public became aware that the company refused to install new equipment (d) The cost savings are likely to be understated by assuming that the premium differential this year applies to all future years If installation of a new system is delayed, premiums might increase even further, and, at some point, coverage might not be available at virtually any price Note to the Instructor: In this slight revision of a problem used in previous editions, we tried to make obvious the issue of risk of harm to employees by describing the insurance coverage and asking specifically about "other" factors It's likely that a few students still will not recognize that issue Some who see it will point out that $8,051 is a small price 7-11 to pay for a serious injury, let alone the life of even one employee Such an assertion presents the opportunity for class discussion of the many situations when efforts are made to place a value on a human life (e.g., court cases and allocations of funds available for medical services) Students should be encouraged to avoid making quick personal judgments about the relative size of some known expenditure (or receipt) Such judgments are especially to be avoided when, as indicated in the parenthetical material in item (b), facts are available to support at least a preliminary assessment of relative magnitude In this case, a preliminary assessment reduces the need to address the more general and more difficult-task of placing a specific value on human suffering Absent analytical evidence that the cost is "relatively small" for the entity in question, a student's assertion to that effect is a personal matter For example, had the negative NPV been, say, $200 million, individual judgments would surely have differed Professor Don Lucy shared with us a suggestion by one of his students that the company tell employees it is spending $200,000 to make them safer 7-25 Employment Options Bob prefers the $2,000,000 for 10 years at his 10% discount rate Pretax flow Less tax at 30% After-tax flow Present value factors Present value Advantage to 10-year term (15-20 minutes) 30 years $1,200,000 360,000 $ 840,000 9.427 $7,918,680 = 10 years $2,000,000 600,000 $1,400,000 6.145 $8,603,000 $684,320 The team prefers $1,200,000 for 30 years at its 14% discount rate Pretax flow Less tax at 40% After-tax flow Present value factors Present value Advantage to 30-year term = $1,217,040 30 years $1,200,000 480,000 720,000 7.003 $5,042,160 10 years $2,000,000 800,000 1,200,000 5.216 $6,259,200 Bob wants a higher present value and the team wants a lower present value It's not surprising that their interests are opposed The team's higher discount rate leads it to prefer lower flows over a longer period, and its higher tax rate works in the same direction Even if they used the same discount rate, their responses could differ because of the tax differences Note to the Instructor: You might extend this assignment by asking whether the team might benefit by raising the 30-year payment so that Bob would prefer it to the 10-year term The 30-year payment that would make Bob indifferent between the choices is $325,926 Present value of 10-year payments (above) Divided by Bob's present value factor for 30 years Annual after-tax payment required Divided by (1 - 30% tax rate) Equals required payment Present value of payment to team ($1,303,702 x 60 x 7.003) 7-12 $8,603,000 9.427 $ 912,592 70% $1,303,702 $5,477,898 The $5,477,898 present value is less than the $6,259,200 of the $2,000,000 for 10 years, so the team could pay more than $1,303,702 over the 30 years and be better off The maximum that the team could pay over 30 years is $372,411 Present Divided Maximum Divided 7-26 value of 10-year payments by factor for 30 years after-tax payment by 60% = maximum pretax payment Importance of Depreciation Period $6,259,200 7.003 $ 893,788 $1,489,647 (15-20 minutes) Negative $1,434 Tax $30,000 20,000 10,000 $ 4,000 Savings in cash operating costs Less depreciation, $100,000/5 Increased taxable income Income tax at 40% Net cash flow Present value factor, years, 10% Present value of future cash flows Investment Net present value Cash Flow $ 30,000 4,000 $ 26,000 3.791 $ 98,566 100,000 ($ 1,434) $2,920, an increase of $4,354 ($2,920 + $1,434) Year Operating savings $30,000 $30,000 $30,000 $30,000 $30,000 Depreciation 50,000 50,000 Change in income (20,000) (20,000) 30,000 30,000 30,000 Tax at 40% ( 8,000) ( 8,000) 12,000 12,000 12,000 Net cash flow* $38,000 $38,000 $18,000 $18,000 $18,000 PV factors 909 826 751 683 621 Present values $34,542 $31,388 $13,518 $12,294 $11,178 NPV = $2,920, total present value of $102,920 less investment of $100,000 * Net cash flow equals operating savings less tax expense (plus tax saving) Note to the Instructor: Instructors who, like the authors, prefer that students not spend time on the computational details associated with MACRS or other accelerated depreciation methods can assign this problem to illustrate the principle of increased NPV 7-27 Introducing a New Product (20-25 minutes) $286,000 Increase Increase Increase Increase Increase Increase Increase in in in in in in in contribution margin (10,000 x $52) cash fixed costs taxable income before depreciation depreciation ($800,000/5) taxable income income taxes at 30% after-tax cash flow Tax $520,000 180,000 340,000 160,000 180,000 $ 54,000 Cash Flow $520,000 180,000 340,000 54,000 $286,000 2.797 years ($800,000/$286,000) About 23.1% using Lotus 1-2-3 Students using tables will see that the rate is between 22% and 24% 7-13 $181,838 Increase in annual after-tax cash flow (requirement 1) Times present value factor for years at 14% Equals total present value of future cash flows Less investment NPV $286,000 3.433 $981,838 800,000 $181,838 (a) BDR should not use the 11% interest rate to determine the present value A return sufficient only to cover the cost of a specific debt-funding source provides no return to the stockholders, and the company must earn a satisfactory return for all its investors, both creditors and stockholders Note also that the source of debt capital for a specific project seldom will provide 100% of the funds needed for an investment, which means owners must provide the rest and will expect a return on their investment Moreover, both creditors and stockholders monitor a company's solvency by watching such factors as the ratio of debt to equity, and the cost of obtaining capital from either source is likely to rise as a company takes on more debt (b) BDR should not include the annual interest payments in computing annual cash flow Discounting provides for both return of capital and a return on capital at least equal to the discount rate Including interest in the cash flows would provide twice for the cost of funds Note to the Instructor: In covering requirement (a) we try to avoid extended discussion of the concept of cost of capital One idea that seems to make sense to introductory students is that money is a fungible good Applying this idea, a company obtaining funds from a variety of sources has a pool of money, no part of which is identifiable by its source To avoid questions that might be raised later by students studying real estate, we usually point out, after covering (a) and (b), that the analysis of single-project real estate investments for potential equity investors is a special case of investment evaluation (a) If the applicable tax rate is constant, accelerating depreciation for tax purposes does not change the total taxes paid However, the higher tax deductions in earlier years would shift the cash outflows for taxes to later years, so the present value of the cash outflows would be lower and the NPV of the project higher (b) The payback period would be shorter because the net cash inflows would be higher in earlier years of the project's life 7-28 Manufacturing Cells, JIT (20 minutes) $2,536.4 thousand, from calculations (in thousands) below Cost savings ($6,579.6 - $4,718.2) Tax on savings, at 40% Net savings Present value factor, 20 years, 12% Present value of savings Depreciation and amortization ($7.5 million/10) $ 750.0 Tax saving at 40% $ 300.0 Present value factor, 10 years, 12% 5.650 Present value of tax savings Present value of all future flows Less investment Net present value 7-14 $ 1,861.4 744.6 1,116.8 7.469 $ 8,341.4 1,695.0 $10,036.4 7,500.0 $ 2,536.4 Note to the Instructor: Chapter specifically addresses treatment of one of the principal features of JIT, near-zero inventories, in a capitalbudgeting decision 7-29 Retirement Options (10-15 minutes) Waddlum's major concern is how long he will live after retirement Spending $80,000 per year, he will go broke in the ninth year if he takes the lump-sum payment Thus, if he lived longer than nine years, he would be better off taking the $60,000 per year and living less comfortably than he prefers If he took the lump-sum payment, he would use $80,000 for expenses the first year, leaving $420,000 to be invested at 10% That investment allows nine withdrawals of $80,000, determined as follows Investment Divided by annual withdrawals Equals present value factor for annuity $420,000 $ 80,000 5.25 The number of periods in the 10% column with the factor closest to 5.25 is eight (a factor of 5.335), which means he could make nine withdrawals of $80,000 (including the first) plus one of about $65,000 in the last year The $80,000 used immediately, plus the eight future withdrawals covers nine years of retirement Note to the Instructor: This problem was made relatively simple by leaving out the many other options For example, pension plans provide for payments to survivors after the death of the retiree Class discussion of this exercise can emphasize how very difficult real-life decisions can be where an estate or other provision for survivors is desired Still, determining the number of years you can live as you wish from the lump-sum investment seems to us a sensible first step in evaluating the options 7-30 Expanding a Product Line (30 minutes) The desk should be introduced The net present value is $92,200 Sales (5,000 x $300) Variable costs at $120 Contribution margin at $260 Fixed cash operating costs Cash flow, before taxes Depreciation ($1.5 million/5) Increase in taxable income Increased taxes (40%) Increase in net cash flow Present value factor, years, 10% Present value of future cash flows Investment Net present value About 3.57 years Tax $1,500.0 600.0 900.0 400.0 500.0 300.0 200.0 $ 80.0 Cash Flows $1,500.0 600.0 900.0 400.0 500.0 80.0 420.0 3.791 $1,592.2 1,500.0 $ 92.2 $ ($1,500.0/$420.0) About 12.4% from Lotus 1-2-3 Students using tables will see that the rate is about 12% The factor 3.57 lies just below 3.605, the factor for 12% 7-15 7-31 Buying Air Pumps (15-20 minutes) The memo should present a recommendation to buy the pumps and the NPV of the purchase alternative (shown below) The memo could also include a brief comment on the implications of a change in the lease payments Lease pumps Revenue Operating expenses Lease expense Total expenses Income before taxes $2,400 $550 850 1,400 $1,000 Buy versus lease Tax $850 500 350 $140 Annual lease savings Less depreciation ($1,500/3) Increase in taxable income Increase in income tax (40%) Net cash flow Present value factor, years, 10% Present value of future flows Less investment Net present value in favor of buying Cash Flow $ 850 140 710 2.487 $1,766 1,500 $ 266 $ Note to the Instructor: The chapter points out that financing and investing decisions should be separated This is an apparent exception, though we not view a year-to-year lease as a financing arrangement Note also that the company has already decided to acquire the air pumps Moreover, revenues exceed operating costs and lease payments, so acquiring the pumps is profitable Hence, the only question is how to acquire them (Some students will not see this point and will spend time trying to develop separate NPV analyses for the two alternatives.) 7-32 Charitable Donation (15-20 minutes) $976,404 ($6,000,000/6.145, the present value factor for a 10-year annuity at 10%) The lump sum, because her discount rate is lower than the university's Pay $6,000,000 now: Outflow Tax saving at 35% Net cash outflow $6,000,000 2,100,000 $3,900,000 Pay $976,404 annually: Donation Tax saving at 35% Net cash outflow Present value factor, 9%, 10 years Present value of outflows Difference (in favor of lump-sum payment) 7-33 Increasing Capacity $ $ 976,404 341,741 634,663 6.418 4,073,267 173,267 $ (25 minutes) A 200,000 increase in volume is not enough to justify the investment 7-16 Tax $600,000 200,000 400,000 240,000 160,000 $ 64,000 Contribution margin (200,000 x $3) Cash fixed costs Pretax cash flow Depreciation ($1,200,000/5) Increase in pretax income Income tax at 40% Net cash flow Present value factor, years, 14% Present value of future flows Investment Net present value Cash Flows $ 600,000 200,000 400,000 64,000 336,000 3.433 $1,153,488 1,200,000 ($ 46,512) $ A 250,000 increase in volume is enough to justify the investment Tax $750,000 200,000 550,000 Contribution margin (250,000 x $3) Cash fixed costs Pretax cash flow Depreciation ($1,200,000/5) Increase in pretax income Income tax at 40% Net cash flow Present value factor, years, 14% Present value of future flows Investment Net present value 310,000 $124,000 Cash Flows $ 750,000 200,000 550,000 240,000 124,000 426,000 3.433 $1,462,458 1,200,000 $ 262,458 $ Note to the Instructor: You might wish to point out that requirement can be solved by looking at differences The additional 50,000 pairs give: Additional contribution margin (50,000 x $3) Times (1 - 40% tax rate) Equals after-tax cash flow Times relevant present value factor Equals additional NPV $150,000 60% $ 90,000 3.433 $308,970 The $308,970 plus the negative $46,512 add up to $262,458 7-34 Funding a Pension Plan (15 minutes) Cash Flows $ 25,000 10,000 $ 15,000 4.833 $ 72,495 60% $120,825 Annual cash outflows Less tax savings at 40% Net cash outflows Present value factor for 10 years at 16% Present value of outflows Divided by (1 - 40% tax rate) Equals maximum before-tax amount 7-35 Research and Development Investment (15-20 minutes) The investment is desirable, NPV of $1.15 million, IRR of about 14.5% 7-17 Year Cash Flow 20X1 20X2 20X3 20X4 20X5 20X6 20X7 20X8 NPV -$4.5 - 6.2 - 8.5 - 3.2 7.0 9.0 11.0 13.0 After-Tax PV Factor -$2.7 - 3.72 - 5.1 - 1.92 4.2 5.4 6.6 7.8 1.000 893 797 712 636 567 507 452 Present Value -$2.70 - 3.32 - 4.07 - 1.37 2.67 3.06 3.35 3.53 $1.15 This assignment differs from others in that it does not have a single investment at time zero Students should still see that the NPV is the present value of all cash flows For convenience, the chapter refers to future flows and investment 7-36 CapitalBudgetingby a Municipality (20 minutes) The center should be built; the net present value of the project is $3,893,400 Rentals of space, etc Tax receipts* Total receipts to city Operating costs Net cash flows Present value factor for 30-year annuity at 8% Present value of future receipts Less investment required NPV $ 1,800,000 1,000,000 2,800,000 500,000 $ 2,300,000 11.258 $25,893,400 22,000,000 $ 3,893,400 * 200,000 persons spending $500 each gives $100,000,000 in spending per year, and the city collects 1% of this sum, or $1,000,000 Like all not-for-profit entities, a city is not trying to provide a return to owners as a business entity must Rather, its purpose is to provide services for which the residents and others will pay and from which they will receive benefits Thus, the only element of cost of capital is the interest rate Note to the Instructor: We ask students whether the investment should be made even if it would not directly pay for itself (say if the cost were $28,000,000) Some suggest that there are likely to be fringe benefits to the city's businesses Some suggest that having the convention center could stimulate tax receipts by attracting other tax-paying businesses to the city That suggestion prompts other students to point out the likelihood of additional costs (e.g., for added police and fire protection) if the city grows as a result of the center There are likely to be some students who will argue that a convention center and possible growth are the last things a city needs Overcrowding, congestion, pollution, and other undesirable features could emerge from the building of the center Additionally the estimates are very subjective Hence the initial question eventually leads students to recognize the possibility of conflict between qualitative and quantitative factors 7-37 Comparison of NPV and Profit (25-30 minutes) The capital-intensive process gives the higher income Labor 7-18 Capital Intensive $5,000,000 2,000,000 3,000,000 1,400,000 1,600,000 640,000 $ 960,000 Sales (100,000 x $50) Variable costs at $20, $10 Contribution margin Fixed costs* Taxable income Income taxes (40%) Net income Intensive $5,000,000 1,000,000 4,000,000 2,100,000 1,900,000 760,000 $1,140,000 * $400,000 + ($4,000,000/4); $600,000 + ($6,000,000/4) The labor-intensive process gives the higher book rate of return on average investment Labor Capital Intensive Intensive Net income $ 960,000 $1,140,000 Divided by average investment $2,000,000 $3,000,000 Equals book rate of return 48% 38% The labor intensive process has the higher NPV Labor Capital Intensive Intensive Contribution margin from requirement $3,000,000 $4,000,000 Fixed cash operating costs 400,000 600,000 Change in pretax cash flow 2,600,000 3,400,000 Depreciation ($4,000,000/4; $6,000,000/4) 1,000,000 1,500,000 Increase in taxable income 1,600,000 1,900,000 Increased taxes (40%) 640,000 760,000 Increase in net income 960,000 1,140,000 Add back depreciation (not a cash flow) 1,000,000 1,500,000 Net cash flow $1,960,000 $2,640,000 Present value factor, years, 16% 2.798 2.798 Present value of future cash flows $5,484,080 $7,386,720 Investment required 4,000,000 6,000,000 Net present value $1,484,080 $1,386,720 Difference in NPVs = $97,360 The memo should report the NPVs of the two alternatives and express a preference for the labor-intensive process because of its higher NPV The memo should also note the relatively small difference between the NPVs and urge further consideration of qualitative factors that might tip the decision one way or the other The memo should emphasize that the preference was based on NPV rather than book rate of return, and it could point out that book rates of return overstate the differences between the two alternatives 7-38 CapitalBudgeting for a Computer Service Company Additional revenues (12 x $40,000) Additional cash expenses (12 x $4,000) Cash flow before taxes Depreciation (given) Income before taxes Income taxes, 40% Net cash flow after taxes Present value factor, years, 16% Present value of future annual cash flows Present value of salvage value ($300,000 x 552) Total present value of investment Investment Net present value 7-39 Reevaluating an Investment (20 minutes) 7-19 (25 minutes) Tax $480,000 48,000 432,000 225,000 207,000 $ 82,800 Cash Flows $ 480,000 48,000 432,000 82,800 349,200 2.798 $ 977,062 165,600 1,142,662 1,200,000 ($ 57,338) $ An analysis using discounted cash flow techniques shows that the investment was unwise Both NPV and IRR suggest the same answer Net present value method Annual cost savings Depreciation Increase in taxable income Income tax at 40% rate Net cash flow Present value factor, 10 years, 16% Present value of returns Investment Net present value Tax $69,000 25,000 44,000 $17,600 Cash Flows $ 69,000 17,600 $ 51,400 4.833 $248,416 250,000 ($ 1,584) Note to the Instructor: It's important to point out that the wisdom of the original investment decision has no bearing on whether the machinery should be replaced now Similar machinery purchased now might yield a return greater than 16% What can be said is that if the machinery available now would cost $250,000, have a 10-year life with no salvage value, provide $69,000 in savings, and be depreciated using the straight-line method, it is unwise to buy it, though just barely 7-40 Purchase Commitment (20-25 minutes) The offer should be rejected because NPV is a negative $87,320 Annual cash flows Interest ($2,000,000 x 8%) Savings in purchase price [($1.00 - $.80) x 1,000,000] Total Less additional income tax at 40% Net after-tax cash flow Present value factor, years, 12% Present value of annual flows Present value of loan repayment ($2,000,000 x 567) Total present value Investment NPV $ 160,000 200,000 360,000 144,000 $ 216,000 3.605 $ 778,680 1,134,000 1,912,680 2,000,000 ($ 87,320) $1.04037 Required investment Present value of loan repayment (from requirement 1) Required present value of annual cash flows Divided by present value factor, years, 12% Equals required after-tax cash flows Divided by (1 - the 40% tax rate) Equals required pretax cash flows Less interest receipts Equals required annual savings in copper price Divided by annual maximum purchases Equals required savings per pound Plus price of copper from Boa Equals required market price $2,000,000 1,134,000 $ 866,000 3.605 $ 240,222 60% $ 400,370 160,000 $ 240,370 1,000,000 $ 24037 80000 $ 1.04037 Note to the Instructor: We use the term "relevant discount rate" because the loan is a relatively riskless investment, or at least one that is less risky than those normally encountered by the firm The discount rate 7-20 should probably be the cost of capital, but using a lower rate might be desirable depending on the credit worthiness of Boa Company One could also argue that this type of investment is extremely risky taken as a whole because its success depends on estimates of the prices of a raw material the price of which is known to fluctuate greatly The problem provides the opportunity to discuss how managers might predict future prices of copper and to lead into the topic of sensitivity analysis in Chapter 7-41 New Product−Complementary Effects (25 minutes) The product should be introduced; the investment's NPV is $8,551,320 Tax Cash Flows Contribution margin, new cleaner ($22 - $12) x 800,000 $8,000,000 $ 8,000,000 Lost contribution margin, lost sales of existing product, ($15 - $9) x 300,000 1,800,000 1,800,000 Net additional contribution margin 6,200,000 6,200,000 Additional cash operating costs 1,400,000 1,400,000 Cash flow before taxes 4,800,000 4,800,000 Less depreciation, $10,000,000/10 1,000,000 Increase in taxable income 3,800,000 Income tax at 40% $1,520,000 1,520,000 Net cash operating flows $ 3,280,000 Present value factor 12%, 10 years 5.650 Present value of future operating flows $18,532,000 Present value of salvage value ($100,000 x 60% x 322) 19,320 Total present value 18,551,320 Investment 10,000,000 Net present value $ 8,551,320 7-42 Discounts and Cash Flows (20 minutes) No, $50 is less than the present value of two $28 payments Present value of $28 in one year ($28 x 893) Present value of $28 now Total present value $25.004 28.000 $53.004 The assumption of 100% renewals for the second year is critical to seeing the question as a comparison of the present values of two cash inflow options Both the costs and the quantity sold (number of subscription-years) are the same for the two subscription plans Hence, the magazine has no reason to offer the extended subscription at a rate that is not equivalent to what it would receive from a one-year subscription plus renewal $53.00, the present value of two $28 payments Yes, the NPV is $310.70 with the two-year subscription, $276.44 with the one year The $50 rate increases total volume enough to offset the expected loss of subscriptions after the first year The calculations below use a batch of 10, as suggested in the assignment Receipts today from two-year subscriptions (10 x $50) Present value of variable cost {[$10 + ($10 x 893)] x 10} Net present value $500.00 189.30 $310.70 Receipts today from 10 one-year subscriptions (10 x $28) $280.00 7-21 Present value of renewals ($28 x 893 x 6) Total present value Present value of variable costs [($10 x 10) + ($10 x x 893)] Net present value 150.02 430.02 153.58 $276.44 About $46.57 This part requires restating the two-year analysis above with the NPV of the one-year subscriptions as the required NPV NPV of one-year subscriptions Plus present value of variable costs, two-year (above) Total required present value Divided by 10 equals required two-year rate $276.44 189.30 $465.74 $ 46.57 Note to the Instructor: The situation in this assignment is familiar to students and to anyone else on mailing lists You might point out that advertising is a major source of revenue to magazines and that advertising rates depend to a great extent on paid circulation Therefore, the magazine could earn more, by way of higher ad rates, if offering a bargain two-year rate keeps subscribers for a longer time The company in this problem might be able to offer a two-year rate even lower than the $46.57 computed in requirement determined that the higher advertising rates commanded by the higher circulation would offset the lower rate 7-43 Quality Improvement (15-20 minutes) About $3.16 million, from calculations (in millions) below Savings in variable costs ($58.0 x 10) Less additional cash fixed costs Pretax cash flow Depreciation ($6.5/5) Increase in taxable income Income tax at 40% Net cash flow Present value factor, years, 12% Present value of future flows Investment Net present value Tax $5.80 2.20 3.60 1.30 2.30 $0.92 Cash Flow $5.80 2.20 3.60 0.92 2.68 3.605 $9.66 6.50 $3.16 About $16.1 million, from the following calculations (in millions) Additional revenue* ($117.8 x 10) Less additional cash fixed costs** Pretax cash flow Depreciation ($6.5/5) Increase in taxable income Income tax at 40% Net cash flow Present value factor, years, 12% Present value of future flows Investment Net present value Tax $11.78 2.20 9.58 1.30 8.28 $ 3.31 Cash Flow $11.78 2.20 9.58 3.31 $ 6.27 3.605 $22.60 6.50 $16.10 * The company gains revenue by selling formerly spoiled units **Total variable costs remain constant because the factory works at the same rate 7-44 Long-Term Special Order (35 minutes) 7-22 The memo should report that (1) accepting the order is wise even if the company cannot increase capacity; (2) the NPV of undertaking the expansion is a negative $10,742; and (3) the proposed limited expansion is probably unwise because it allows the company to recover only the 10,000 units of regular sales lost by accepting the order Accept the order without expanding Contribution margin as is [200,000 x ($12 - $7)] Contribution margin if order accepted: 190,000* x ($12 - $7) 40,000 x ($9 - $7) Total if order accepted $1,000,000 $ 950,000 80,000 $1,030,000 * Capacity of 230,000 units - 40,000 for special order = 190,000 for sales at regular prices Accept the order and expand Increased contribution margin (10,000 x $5) Increased fixed costs Increased cash flow before taxes Depreciation ($100,000/5) Increase in taxable income Taxes (40%) Net change in cash flow after taxes Present value factor, years, 14% Present value of future cash inflows Investment required Net present value 7-45 Analyzing a New Product Tax $50,000 20,000 30,000 20,000 10,000 $ 4,000 Cash Flow $ 50,000 20,000 30,000 4,000 $ 26,000 3.433 $ 89,258 100,000 ($ 10,742) (40-45 minutes) The investment has an NPV of $1,616,712 Tax Revenue (30,000 x $90) $2,700,000 Variable costs: Materials (30,000 x $10) 300,000 Labor (30,000 x $17) 510,000 Variable overhead (30,000 x $10*) 300,000 Commissions (30,000 x $4) 120,000 Total (30,000 x $41) 1,230,000 Contribution margin (30,000 x $49) 1,470,000 Cash fixed costs 200,000 Pretax cash flow 1,270,000 Depreciation ($3,000,000/10) 300,000 Increase in pretax income $ 970,000 Income tax at 40% $ 388,000 Net cash flow Present value factor, 10 years, 14% Present value of future flows Present value of salvage** ($100,000 x 60 x 270) Total present value Investment Net present value * Calculation of variable overhead per unit: 7-23 Cash Flows $2,700,000 300,000 510,000 300,000 120,000 1,230,000 1,470,000 200,000 1,270,000 388,000 882,000 5.216 $4,600,512 16,200 4,616,712 3,000,000 $1,616,712 $ Total overhead per unit Less fixed overhead per unit Variable overhead per unit ($600,000/30,000) $30 20 $10 **Residual value is taxable because the full cost was depreciated over the project's useful life Barker's analysis is deficient in the following ways (a) The existing fixed manufacturing costs allocated to the new product are sunk and irrelevant Only the $200,000 incremental amount is relevant (b) The allocated selling and administrative expenses are likewise irrelevant Only the $4 commission is relevant (c) The $900,000 already spent for research and development is a classic example of a sunk cost and is irrelevant (d) Barker ignored the salvage value, though it should be included in the calculation The item is not large in this case, but it could be significant in another 7-24 ... $286,000 Increase Increase Increase Increase Increase Increase Increase in in in in in in in contribution margin (10,000 x $52) cash fixed costs taxable income before depreciation depreciation ($800,000/5)... rationing, sensitivity analysis, and mutually exclusive alternatives in Chapter We leave to courses in managerial finance the task of discussing the significance and calculation of cost of capital. .. book-rate-of-return rankings not necessarily indicate relative profitability B is the only desirable investment, using discounted cash flow analysis Investment A illustrates that payback ignores profitability;